Details

analyze129.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Rules

785×	`distribute-rgt-neg-in_binary64`
770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
289×	`sub-neg_binary64`
232×	`associate-+l+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	29	25
2	50	25
3	138	25
4	374	25
5	1117	25
6	2839	25
7	5140	25

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite112.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64` `add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
3×	`unpow-prod-down_binary64` `pow-unpow_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`

Counts

4 → 59

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
5.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(+.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 1430 to 623 computations (56.4% saved)

series192.0ms (4.6%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

80.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
49.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
25.0ms	(+.f64 (.f64 a a) (.f64 b b))
9.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1774 to 1392 computations (21.5% saved)

simplify147.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-l_binary64`
585×	`associate-r_binary64`
408×	`distribute-rgt-neg-in_binary64`
301×	`exp-prod_binary64`
242×	`distribute-rgt-in_binary64`

Counts

110 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1770
1	301	1632
2	857	1626
3	3572	1626
4	4721	1626
5	4972	1626
6	4881	1626

prune58.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Error

0.0b

Counts

75 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
	16.2b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)) 1)

Compiler

Compiled 940 to 487 computations (48.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
0.0b	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
2.1b	(.f64 (.f64 a a) (*.f64 b b))

rewrite179.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

50×	`pow1_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow-prod-down_binary64`
21×	`prod-exp_binary64` `cbrt-unprod_binary64`
18×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
22.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
13.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
10.0ms	(.f64 (.f64 a a) (*.f64 b b))

Compiler

Compiled 2566 to 1319 computations (48.6% saved)

series207.0ms (5%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

80.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
67.0ms	(+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
25.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
23.0ms	(.f64 (.f64 a a) (*.f64 b b))

Compiler

Compiled 1930 to 1519 computations (21.3% saved)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Rules

786×	`distribute-rgt-in_binary64`
731×	`distribute-lft-in_binary64`
274×	`cancel-sign-sub-inv_binary64`
207×	`associate-r_binary64`
205×	`associate-l_binary64`

Counts

131 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2692
1	344	2435
2	1490	2302
3	5004	2302

prune50.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	80	3	83

Error

0.0b

Counts

83 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
	16.2b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)) 1)

Compiler

Compiled 1013 to 608 computations (40% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
0.3b	(.f64 (.f64 b b) (cbrt.f64 4))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite185.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

38×	`pow1_binary64`
33×	`add-exp-log_binary64`
26×	`add-sqr-sqrt_binary64`
20×	`pow-prod-down_binary64` `cbrt-prod_binary64`
19×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
10.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
6.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 2925 to 1816 computations (37.9% saved)

series95.0ms (2.3%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

55.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
16.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))
11.0ms	(.f64 (.f64 b b) (cbrt.f64 4))
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

Compiler

Compiled 1198 to 971 computations (18.9% saved)

simplify126.0ms (3%)

Algorithm

1×	egg-herbie

Rules

374×	`*-commutative_binary64`
358×	`sqr-pow_binary64`
354×	`associate-/l*_binary64`
318×	`exp-prod_binary64`
236×	`log-prod_binary64`

Counts

133 → 97

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	139	2016
1	275	1516
2	816	1478
3	1566	1461
4	2961	1369
5	4540	1369
6	4892	1369

prune59.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Error

0.0b

Counts

100 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
▶	16.2b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)) 1)

Compiler

Compiled 1210 to 744 computations (38.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.2b	(pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
30.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3))

rewrite130.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-cube-cbrt_binary64` `cbrt-prod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `cube-prod_binary64` `pow-unpow_binary64`
5×	`add-cbrt-cube_binary64`
4×	`cube-div_binary64`

Counts

4 → 77

Calls

4 calls:

13.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3))
11.0ms	(pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(+.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 2282 to 1111 computations (51.3% saved)

series303.0ms (7.3%)

Error

0.0b

Counts

4 → 68

Calls

4 calls:

92.0ms	(pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)
78.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3))
53.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
28.0ms	(+.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 3324 to 2697 computations (18.9% saved)

simplify146.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

575×	`unswap-sqr_binary64`
284×	`distribute-rgt-out_binary64`
276×	`exp-prod_binary64`
244×	`associate-+r+_binary64`
228×	`associate-r_binary64`

Counts

145 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	4161
1	623	3714
2	2422	3626
3	4600	3626
4	5034	3626

prune92.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	116	3	119

Error

0.0b

Counts

119 → 3

Alt Table

Status	Error	Program
	0.0b	(-.f64 (+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b))) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (.f64 b b) (cbrt.f64 4)))) 1)
	16.2b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)) 1)

Compiler

Compiled 1869 to 1086 computations (41.9% saved)

regimes1.1s (26.1%)

Accuracy

Total 0.0b remaining (33.1%)

Threshold costs 0.0b (33.1%)

Compiler

Compiled 20474 to 13597 computations (33.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64` `sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	29	37
2	30	37
3	28	37

end1.0ms (0%)

Compiler: Compiled 27 to 21 computations (22.2% saved)

sample678.0ms (16.2%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 124 to 88 computations (29% saved)

Details

analyze129.0ms (3.1%)

sample19.0ms (0.4%)

simplify41.0ms (1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite112.0ms (2.7%)

series192.0ms (4.6%)

simplify147.0ms (3.5%)

prune58.0ms (1.4%)

localize14.0ms (0.3%)

rewrite179.0ms (4.3%)

series207.0ms (5%)

simplify82.0ms (2%)

prune50.0ms (1.2%)

localize13.0ms (0.3%)

rewrite185.0ms (4.4%)

series95.0ms (2.3%)

simplify126.0ms (3%)

prune59.0ms (1.4%)

localize12.0ms (0.3%)

rewrite130.0ms (3.1%)

series303.0ms (7.3%)

simplify146.0ms (3.5%)

prune92.0ms (2.2%)

regimes1.1s (26.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample678.0ms (16.2%)

Profiling